The nature of the Virasoro algebra was described by
Kupershmidt [1]}. Its applications in mathematics and physics, such that in conformal field theory and string theory were also presented [2]}, [3]}, [1]}. Many generalizations and deformations (one or two parameters) of the Virasoro algebra were investigated in the literature[5]}, [6]}, [7]}.
The generalization of Kupershmidt's work was provided in [1]}.
The relation between the Korteweg-de Vries (KdV) equation and the Virasoro algebra was described by Gervais [9]} and Kupershmidt [1]}. Moreover,
Huang and Zhdanov presented the realizations of Witt and Virasoro algebras. Their connection with integrable equations was determined[11]}.
